Noise Spectrum Notch Generation with Pulse Coding Control and EMI Noise Reduction Technology of DC-DC Switching Converter

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Noise Spectrum Notch Generation with Pulse Coding Control and EMI Noise Reduction

Technology of DC-DC Switching Converter

YIFEI SUN

PhD Dissertation

DIVISION OF ELECTRONICS & INFORMATICS GRADUATE SCHOOL OF SCIENCE & TECHNOLOGY

GUNMA UNIVERSITY JAPAN

March 2020

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Noise Spectrum Notch Generation with Pulse Coding Control and EMI Noise Reduction Technology

of DC-DC Switching Converter

DISSERTATION Submitted by

YIFEI SUN

In partial fulfillment of the requirements for the award of the Degree of

DOCTOR OF PHILOSOPHY IN

ELECTRONICS & INFORMATICS ENGINEERING

Under the guidance of

PROFESSOR HARUO KOBAYASHI, Ph. D. Eng.

DIVISION OF ELECTRONICS & INFORMATICS GRADUATE SCHOOL OF SCIENCE & TECHNOLOGY

GUNMA UNIVERSITY JAPAN

March 2020

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Acknowledgement

I would like to express my deepest appreciation to all those who provided me the possibility to complete this dissertation.

Special thanks to my supervisor Professor Dr. Haruo KOBAYASHI for his great guidance and encouragement. He not only taught me knowledge, but also taught me to become a good human. I would like to express my appreciation to Professor Yasunori KOBORI for his great guidance and advice. He promotes my internal motivation on research and encourages me to achieve the research goals with the right set of planning and measured steps. I would like to thank Professor Anna KUWANA for her kind advice. I would also like to thank Professors Masashi OCHIAI, Jun-ichi MATSUDA for valuable discussions. Additionally, I would like to thank Mr. Nobuyoshi ISHIKAWA for their help in procuring lab equipment and managing funding.

I am thankful to the members of our Laboratory. Thanks to Jianlong WANG for his valuable help on my research and daily life. Thanks to Tran MINH TRI, Noriyuki OIWA, Shogo KATAYAMA for their valuable discussion and advice. Thanks to Jing LI, Dan YAO, Shiyu WANG, Yujie ZHAO for their help in my Japanese communication. I would also like to thank Rino TAKAHASHI, as my Japanese tutor, her teach me Japanese language and culture.

I was greatly assisted by the Gunma University Human Resources Cultivation Center as a research assistant from 2018-2020. Thanks to Prof. Kenichi KASUYA, Prof.

Kuniyuki MOTOJIMA, Coordinator Kumiko TAURA and Seretary Nami SAKAGUCHI.

Furthermore, I would like to thank my alma mater Shenyang University of Chemical Technology and Professor Decheng YUAN who is my master degree supervisor, who gives me the opportunity to go abroad, learning advanced technology, given me a rational look at the world.

Finally, sincerely thank to my parent Mei LI and Rong SUN. Thanks for their endless love and all that they did for me. Thanks to Zhe XU, who gives me courage and spiritual support.

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Declaration

I hereby declare that this submission is my own work and that, to the best of my knowledge and belief, it contains no material previously published or written by another person, nor material which has been accepted for the award of any other degree of the university or other institute of higher learning, except where due acknowledgement has been made in the text.

Signature:

Name: YIFEI SUN Student No.:

Date:

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Abstract

This dissertation deals with the reduction of Electromagnetic Interference (EMI) in the DC-DC switching converter for the communication equipment. Simultaneously, a novel EMI spread spectrum technology is proposed that does not distribute the switching noise into some specified frequency bands.

For reducing the switching noise of DC-DC switching converter, we often use frequency modulation of the clock. But in the hysteretic control convert with Constant-On Time (COT) pulse and ripple injection method or soft switching converter, there is no fixed clock pulse. For these clock-less switching converter, we have developed techniques to reduce EMI noise. In this case, the modified ripple is also increased and it is corrected by developed ripple reduction method.

In the Pulse Width Modulation (PWM) method for switching converter also causes EMI noise on its clock frequency and harmonics. In order to reduce the EMI noise, modulation of the clock pulse is used by shaking the phase or frequency of the clock.

Since the energy of clock frequency and its high frequency harmonics can be diffused to other frequencies, the peak level of the clock spectrum is low and there is no line spectrum at the frequency of the clock and its harmonic spectra, but the bottom level (floor noise) is high. Therefore, we have created an EMI spread spectrum technique with both EMI reduction and noise diffusion based on Spread-Spectrum Clock Generator (SSCG) uses a Delta-sigma (ΔΣ) Digital-to-Time Converter (DTC) to spread the clock spectrum while allowing us to select the bands that we do not want to spread by predecessors.

In this dissertation we propose an EMI spread spectrum technology with automatically setting of the notch frequency using the pulse coding controlled method in the DC-DC switching converter for the communication equipment. In communication devices, small noise as much as possible is desired at the receiving signal band. We realized the method that notch frequency can be automatically set to the frequency of the received signal by adjusting the clock frequency. Therefore, just let the notch frequency be equal to the received signal frequency suppress noise in the received signal frequency.

Chapter 1 introduces the background, the motivation, and the objectives of this research and the proposed approaches. Chapter 2 discusses the basic topology and basic operation of DC-DC switching converter. Chapter 3 presents proposed EMI reduction and output ripple suppression method. Chapter 4 discusses notch frequency method

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with pulse coding control in switching converter. Chapter 5 describes a full-automatic notch generation of pulse width coding switching converter. Chapter 6 confirmed the notch frequency experimentally with the prototype circuit. Chapter 7 summarizes conclusions obtained through this research and future work is proposed.

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List of Figures

Figure 1.1Circuit structure of spread spectrum clock generator ... 4

Figure 1.2 Spectrum of pulse coding signal. ... 5

Figure 1.3 Modulation figures of PWM. ... 6

Figure 1.4 PWM pulse sequence. ... 6

Figure 1.5 Spectrum of PWM using PWM ∆Σ DTC. ... 7

Figure 2.1 Performance of DC-DC switching converter. ... 9

Figure 2.2 Basic configuration of DC-DC switching converter. ... 10

Figure 2.3 Basic constitution of buck, boost, and buck-boost converters. ... 10

Figure 2.4 Switch state and switching waveform. ... 11

Figure 2.5 Basic circuit of buck converter. ... 12

Figure 2.6 Buck converter when switch (SW) turns on. ... 12

Figure 2.7 Buck converter when switch (SW) turns off. ... 13

Figure 2.8 Timing chart of buck converter (continuous current mode (CCM)). ... 13

Figure 2.9 Voltage-mode negative feedback control circuit. ... 14

Figure 2.10 Waveforms in switching converter. ... 14

Figure 2.11 Basic circuit of power stage. ... 15

Figure 2.12 On-period equivalent circuit. ... 16

Figure 2.13 Off-period equivalent circuit. ... 16

Figure 2.14 CCM block diagram of buck converter. ... 19

Figure 2.15 Bode diagram of the buck converter. ... 20

Figure 2.16 Basic circuit of the boost converter. ... 21

Figure 2.17 Boost converter when switch (SW) turns on. ... 21

Figure 2.18 Boost converter when switch (SW) turns off. ... 22

Figure 2.19 Timing chart of the boost converter (CCM). ... 22

Figure 2.20 Basic circuit of the buck-boost converter. ... 23

Figure 2.21 Buck-boost converter when switch (S) turns on. ... 24

Figure 2.22 Buck-boost converter when switch (S) turns off. ... 24

Figure 2.23 Timing chart of the buck-boost converter. ... 25

Figure 2.24 Basic hysteretic control buck converter. ... 26

Figure 2.25 Operation waveforms of hysteretic control. ... 27

Figure 2.26 COT type hysteretic control buck converter. ... 29

Figure 2.27 Timing chart of COT type hysteretic control buck converter. ... 29

Figure 2.28 Ripple injection method buck converter. ... 30

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Figure 2.29 Waveforms of ripple injection converter. ... 31

Figure 2.30 Voltage and current during hard switching (a): off-process (b): on-process. ... 32

Figure 2.31 Voltage and current during soft switching (a): off-process (b): on-process. ... 32

Figure 2.32 Full-wave resonant soft-switching. ... 34

Figure 2.33 Timing chart of full-wave resonant soft-switching. ... 34

Figure 3.1 Waveforms analysis of a frequency-hopped buck converter with two hopping frequencies. ... 37

Figure 3.2 EMI regulation in radiation noise (CISPR22) in Japan. ... 38

Figure 3.3 Buck converter with PWM signal control. ... 39

Figure 3.4 Simulated spectrum without EMI reduction. ... 39

Figure 3.5 Frequency modulation of buck converter with PWM signal control. .... 40

Figure 3.6 Spectra of modulation converter. ... 41

Figure 3.7 Output ripple with/without modulation. ... 41

Figure 3.8 SAW generator & modified current source. ... 43

Figure 3.9 Comparison of SAW signals. ... 43

Figure 3.10 Modulated and corrected ripple. ... 44

Figure 3.11 COT control method hysteretic control converter. ... 46

Figure 3.12 Waveforms of COT type hysteretic control converter... 46

Figure 3.13 EMI noise reduction with COT control circuit. ... 47

Figure 3.14 Timing chart of modified COT pulse. ... 47

Figure 3.15 COT control method spectrum without EMI reduction. ... 48

Figure 3.16 Spectrum with EMI reduction. ... 49

Figure 3.17 Output ripple with modulation. ... 49

Figure 3.18 Improved EMI noise reduction with the COT control method. ... 50

Figure 3.19 Block diagram of improved EMI noise reduction with the COT converter. ... 50

Figure 3.20 Output ripple with improved EMI noise reduction with the COT converter. ... 51

Figure 3.21 EMI noise reduction with the ripple injection method... 52

Figure 3.22 Spectrum of the ripple injection method hysteretic converter. ... 52

Figure 3.23 Circuit to cancel the output ripple. ... 54

Figure 3.24 Cancellation of the output ripple ... 54

Figure 3.25 Cancellation of the ripple 𝑉𝑜𝑐. ... 55

Figure 3.26 Signals with cancellation... 55

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Figure 3.27 Circuit of the full-wave resonant converter. ... 56

Figure 3.28 EMI reduction modulation circuit. ... 57

Figure 3.29 Simulation waveforms in EMI reduction modulation circuit. ... 57

Figure 3.30 Spectrum of the soft-switching converter output. ... 58

Figure 3.31 Spread spectrum of the soft-switching converter output... 59

Figure 3.32 Waveforms in the ripple cancellation circuit. ... 60

Figure 3.33 Circuit of the output ripple cancellation method... 60

Figure 3.34 Output ripple with EMI reduction (red) and ripple cancellation (green). ... 61

Figure 3.35 ZVS operation waveforms at ripple correction. ... 62

Figure 3.36 ZVS operation improvement circuit. ... 62

Figure 3.37 Waveforms of ZVS operation improvement. ... 62

Figure 3.38 Simulation result of the resonant voltage improvement. ... 63

Figure 3.39 Spectrum of ZVS improvement circuit. ... 63

Figure 4.1 Switching converter with pulse coding. ... 66

Figure 4.2 Buck converter with PWC control. ... 67

Figure 4.3 Main signal waveforms of PWC method. ... 67

Figure 4.4 Main signal waveforms of PWC method. ... 69

Figure 4.5 Spread spectrum with PWC control. ... 69

Figure 4.6 Transient response characteristics of PWC method. ... 69

Figure 4.7 Buck converter with PPC control. ... 70

Figure 4.8 Waveforms of PPC control. ... 71

Figure 4.9 Coded pulses with the PCC method. ... 72

Figure 4.10 Buck converter with PCC control. ... 73

Figure 4.11 Main signal waveforms of PCC method. ... 73

Figure 4.12 Simulation waveforms of PCC method... 74

Figure 4.13 Spectrum of buck converter with PCC control (without EMI reduction). ... 74

Figure 4.14 Buck converter with PWPC control. ... 75

Figure 4.15 Main signal waveforms of PWPC method. ... 76

Figure 4.16 Spectrum of buck converter with PWPC control. ... 76

Figure 4.17 Transient response characteristics of PWPC method. ... 77

Figure 4.18 1 period 2 pulse trains of pulse width coding signal. ... 77

Figure 4.19 1 period 8 pulse trains of pulse width coding signal. ... 79

Figure 4.20 Comparison diagram between theoretical formula and spectrum. ... 80

Figure 4.21 1 period 2 pulse trains of pulse phase coding signal. ... 80

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Figure 4.22 1 period 2 pulse trains of pulse cycle coding signal. ... 81

Figure 4.23 1 period4 pulse trains of pulse width pulse phase coding signal. ... 82

Figure 4.24 Comparison of notch characteristics with PWC method and PWPC method. ... 83

Figure 5.1 Best position of 𝐹𝑛 occurrence. ... 86

Figure 5.2 Timing chart of relationship between Pulse-H and Pulse-L of PWM signals. ... 87

Figure 5.3 Pulse coding of automatic PWC method in 𝑃 = 1 situation. ... 88

Figure 5.4 Pulse coding of automatic PWC method in 𝑃 = 𝑁 situation... 89

Figure 5.5 Simulation waveforms of Pulse-L and Pulse-H generation in 𝑃 = 1 situation. ... 90

Figure 5.6 Simulated spectrum by PWM signal without EMI reduction when 𝑃 = 1 situation. ... 90

Figure 5.7 Simulated spectrum with EMI reduction in 𝑃 = 1 situation. ... 91

Figure 5.8 Simulation waveforms of pulse-H and pulse-L generation in 𝑃 = 2 situation. ... 92

Figure 5.10 Simulation waveforms of Pulse-H and Pulse-L generation in 𝑃 = 3 situation. ... 93

Figure 5.12 Block of change channel 1 to channel 2. ... 94

Figure 5.13 𝐹𝑖𝑛1 = 750𝑘Hz situation. ... 94

Figure 5.14 𝐹𝑖𝑛2 = 1,250𝑘Hz situation. ... 95

Figure 5.15 Automatic switching on transient response and saw-tooth. ... 96

Figure 5.16 Pulse coding of PWPC method. ... 97

Figure 5.17 Timing chart of buck converter with PWPC control. ... 97

Figure 5.18 Waveforms of saw-tooth with period 𝑇𝑐𝑘 and delay 𝑇𝑐𝑘. ... 98

Figure 5.19 Main waveforms of PWPC method. ... 99

Figure 5.20 Simulated spectrum with EMI reduction using PWPC method. ... 99

Figure 5.21 Waveforms of the SEL signal. ... 102

Figure 5.22 Change of the output voltage ripple. ... 103

Figure 5.23 Waveforms of the select signal and ripple of output voltage in 𝐷=0.28 situation. ... 103

Figure 5.24 𝐷 automatic detection circuit. ... 105

Figure 5.25 Main signal waveforms of 𝐷 detection method. ... 105 Figure 5.26 Simulated spectrum with full automatic notch frequency generation

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without EMI reduction. ... 106

Figure 5.27 Select signal waveform with full automatic notch frequency generation. ... 106

Figure 5.28 Output voltage ripple with full automatic notch frequency generation. ... 106

Figure 6.1 Converter with PWC control. ... 109

Figure 6.2 The flowchart for using Kicad software. ... 110

Figure 6.3 PWC control buck converter circuit with Kicad. ... 111

Figure 6.4 PWC control buck converter PCB board. ... 112

Figure 6.5 Waveforms of 𝑊𝐻 and 𝑊𝐿 in PWC control buck converter. ... 113

Figure 6.6 Spectrum of the PWC control switching converter. ... 113

Figure 6.7 Automatic notch frequency generation circuit with Kicad. ... 114

Figure 6.8 Main signal waveforms when using 𝑇𝑖𝑛 create 𝑇𝑐𝑘. ... 115

Figure 6.9 Automatic notch frequency generation PCB board circuit. ... 116

Figure 6.10 Experimental waveforms of 𝑊𝐻 and 𝑊𝐿 (𝐹𝑖𝑛 = 400𝑘𝐻𝑧). ... 117

Figure 6.11 Experimental waveforms of PWM and SEL signals (𝐹𝑖𝑛 = 400𝑘𝐻𝑧). ... 117

Figure 6.12 Simulation spectrum of PWM signal (𝐹𝑖𝑛 = 400𝑘𝐻𝑧). ... 118

Figure 6.13 Experimental spectrum of PWM signal (𝐹𝑖𝑛 = 400𝑘𝐻𝑧). ... 118

Figure 6.14 Experimental waveforms of 𝑊𝐻 and 𝑊𝐿 (𝐹𝑖𝑛 = 600𝑘𝐻𝑧). ... 119

Figure 6.15 Experimental waveforms of PWM and SEL signals (𝐹𝑖𝑛 = 600𝑘𝐻𝑧). ... 119

Figure 6.16 Simulation spectrum of PWM signal (𝐹𝑖𝑛 = 600𝑘𝐻𝑧). ... 119

Figure 6.17 Experimental spectrum of PWM signal (𝐹𝑖𝑛 = 600𝑘𝐻𝑧). ... 120

Figure 6.18 Transient response characteristics of the PWC method. ... 120

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List of Tables

Table 2.1 Parameters of the buck converter. ... 20

Table 3.1Parameter values of simulation circuit. ... 40

Table 3.2 Simulation parameters. ... 43

Table 3.3 Simulation parameters. ... 45

Table 3.4 Parameter values in simulation. ... 58

Table 4.1 Parameter values of PWC control simulation circuit. ... 68

Table 4.2 Parameter values of PCC control simulation circuit. ... 74

Table 6.1 Parameter values of implementation circuit. ... 112

Table 6.2 Parameter values of implementation circuit. ... 116

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1. Introduction

This dissertation describes the results of research on an EMI reduction in the DC-DC switching converter for the communication equipment. Furthermore, we propose a spread spectrum technology that the noise component of a specific frequency could be suppressed. In this chapter, first we introduce the research background. Next, based on the background, we describe how predecessors notice that the notch characteristics appears in the spectrum of the output pulse in the pulse coding system in DTC circuit [1]. Then, the motivation and purpose of this dissertation are explained. The organization of the dissertation is shown in the last section in this chapter.

1.1 Research background

In recent years, switching power supply circuits are used in many electronic devices because of their advantages such as high efficiency, high performance (such as low output ripple and fast transient response), large current output and continuously variable output voltage. Also the communication circuit has been accelerated to be powerful and higher density packaging. However, since the switching power supply circuit is driven by switch with the clock, it will generate large switching noise [2]-[3]. The fluctuation of the switching noise has strongly spread in the wide frequency range with the acceleration of high-speed and high-frequency electronic equipment. So it is very important to reduce EMI noise.

EMI stands for electromagnetic interference. In terms of switching power supplies, the action of switching generates switching noise. In a loop in which currents are suddenly turned on and off during switching, high-frequency ringing (switching noise) occurs due to parasitic components. In order to reduce the switching noise that they generate, complex noise filtering and shielding are needed which make the switching power supply larger in size and costly [4]. For this reason, noise reduction methods that do not use filters are required in many fields, including the automotive field. There are some techniques for broadening and flattening their switching noise power spectrum to reduce EMI and to satisfy EMI regulation [5], such as spread spectrum method that randomly modulates the clock signal [6]-[9]. Spread spectrum of switching power supply means changing the switching frequency in a certain range and distributing noise energy to surrounding frequencies without concentrating on one frequency, lowering the

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peak value of noise and clearing EMI standards, generating noise. The technique to reduce the impact on the equipment such as spread spectrum method that randomly modulates the clock signal is being used. For example, some techniques talk about EMI reduction method with spread spectrum using pseudo analog noise which is produced from M-sequence circuit with PLL circuit [10]. Some techniques talk about digital pseudo-random dithering of the switching, regulator control clock timing, and such clock jitter can be introduced by adding simple digital circuitry [11]. Some techniques talk about using triangular waveform modulation as the spectrum modulation method.

Moreover, some spread spectrum methods talk about chaos-based pulse width modulation [12]-[17].

Although these methods suppressing the peak levels at the fundamental frequency and its harmonic frequencies, there are problems such as ripple of output voltage will increase or the diffusion noise is superimposed on an unwanted band (diffusion band).

Particularly, in the automobile field, the density and complexity of internal electronic circuits are progressing toward electrification and automatic driving. If EMI countermeasures are not taken, noise may be superimposed on the radio band or malfunctions may be induced in other electronic devices. Vehicle noise standards are stricter than consumer products. Not only is the standard itself strict, but it is also required that AM radio sound must not contain noise. For this reason, the switching frequency of the DC-DC converter is preferably 2MHz or higher, which is higher than the AM radio frequency band, but this leads to a demand for high-speed switching and causes further high-frequency noise. In response to EMI standards for in-vehicle equipment, many countermeasures are required. One example of this is that “the switching frequency used in in-vehicle DC-DC converters and their high frequencies must not overlap with the reception frequency band of radio AM, FM” [18].

So we try to consider about some spread spectrum techniques for EMI reduction with suppressing diffusion of power supply noise and decrease output ripple. Moreover, we propose a spread spectrum technique for clock pulse with suppressing diffusion of power supply noise using pulse width coding methods, based on the notch characteristics design. We expect that if notch frequency is set to the frequency of the received signal by adjusting the clock frequency. Therefore, just let the notch frequency be equal to the received signal frequency, it will suppress noise in the received signal frequency and be not affected by other spread spectrum. So in the following part, it will be shown that the occurrence of the notch characteristic by predecessors is the motivation of this research.

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1.2 SSCG for Switching Converter using Digital ∆𝚺 Modulation

Predecessors have suggested an auto-configurable Spread-Spectrum Clock Generator (SSCG) that dynamically changes clocks spread spectrum in a way to eliminate clock speeded collision with other desired signal in neighboring frequency bands. This proposed method uses a Delta-Sigma (ΔΣ) Digital-to-Time Converter (DTC) to spread the clock spectrum while allowing us to select the bands that we do not want to spread.

1.2.1 SSCG using PWM ΔΣ DTC

Constant trend of device miniaturization and functioning frequency has led to rise in ΔΣ modulation methods popularity. The usage of lower resolution signal with higher samples in ΔΣ method simplifies the overall circuit complexity and therefore benefits cost efficiency. ΔΣ modulation converts the analog voltage into a pulse frequency output easily brought to time domain. This coarsely quantized output has found increasing usage in time domain signal processing. In time domain signal processing, variable is always measured and analyzed against time rather than its amplitude. Functions such as electronic signals, market behaviors are some example of time domain values. Time domain signal processing superiority, arguably is due to its lack of requirement for process such as filtering, amplifying and mixing plus its support for prediction and regression of the signal behavior over the time.

Further, time domain signal analysis makes it much easier to work in situation where the aim of analysis is to analyze and solve a time domain related problem; the SSCG in this dissertation is such one [19].

DTC converter is an algorithm to bring and convert digital signals (in voltage domain) to analog signal in time domain by component (period, width, phase) of the pulse according to the value. The process of converting signal from digital to analog usually involves many techniques such as filtering and smoothing of the signal before convention. DTC includes a digital ΔΣ modulator and samples are interpolated with analog low pass filter (LPF). In DTC, LPF is used to smooth the signal by cutting its high frequency components. Output signal is then converted to one-bit resolution timing signal.

DTC output signal spectrum can easily be manipulated by the algorithm and chosen parameters in the conversion process and its usage is found in spread spectrum clock generator and power circuits switching EMI removal [20].

Fig. 1.1 shows the circuit structure of spread spectrum clock generator. A sine wave

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input to ∆Σ modulator, and a square wave with noise shaping is output through the ∆Σ modulator. Identification of this as a digital value of “0” on no modulation situation and

“1” on modulation situation, and the digital value is input to the DTC. The clock signal is modulated according to the digital value that is ΔΣ modulated by the DTC, and the modulated clock signal is output.

Figure 1.1Circuit structure of spread spectrum clock generator

Since the main cause of EMI is created by voltage, current switching synchronized with the circuit clock, in the noise spectrum, power is concentrated at a specific frequency (clock frequency and integral multiple frequency). It will lead to failure to meet EMI regulation. Fig.1.2 (a) shows the spectrum of pulse coding signal using fast Fourier transform (FFT). We can find that clock frequency does not meet EMI regulation. Here by modulating the clock signal using spread spectrum clock generator, the spread spectrum of pulse coding signal as shown in Fig. 1.2 (b). As a result, peak power is reduced and EMI problems can be reduced. However, as application in some signal bands (such as AM radio frequency 𝑓_𝑠), it is not desirable to have noise from the spread clock. If spread spectrum using ΔΣ DTC algorithm implemented in programmatically configurable digital circuit, location of the required exclusion spectrum bands can be sensed and DTC algorithm parameters can change automatically (Fig. 1.2 (c)).

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Figure 1.2 Spectrum of pulse coding signal.

We introduce here that SSCG with proposed PWM ΔΣ DTC methods can adjust emission bands and excluding noise emission in specific bands.

First, Fig. 1.3 (a) shows the waveform without modulation (digital value = “0”). The parameter of the pulse wave is a rectangular wave with a period 𝑇 = 1𝑚𝑠 (frequency:

𝑓 = 1𝑘𝐻𝑧), width 𝑊 = 200𝜇𝑠, phase 𝜃 = 0, duty ratio D = 20%. Pulse Width Modulation (PWM) ∆Σ DTC changes the pulse width of the output signal based on the input digital value. As shown in Fig. 1.3 (b), when the digital value is “1”, the pulse width is set to 𝑊_𝑀 (600𝜇𝑠 in the figure). 𝑊 is the pulse width before modulation, 𝑊_𝑀 is the pulse width after modulation, and let 𝑊_𝑀 be smaller than one period. Fig.

1.4 shows an example of the generated pulse. It represents the pulse train when the ∆Σ modulated value “01011” is input. When D = “0”, no modulation is performed and 𝑊 = 200𝜇𝑠, but when D = “1”, pulse width modulation is performed and 𝑊_𝑀 = 600𝜇𝑠 is modulated.

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Figure 1.3 Modulation figures of PWM.

Figure 1.4 PWM pulse sequence.

1.2.2 Notch Frequency Generation due to Two-Coding Pulse

Fig. 1.5 (a) shows the spectrum of the fundamental PWM (Fig. 1.3 (a)) using FFT. In the PWM method, when the pulse width is 𝑊 = 200𝜇𝑠 when input “0”, the period T=1ms, and 𝑊_𝑀 = 600𝜇𝑠 when input “1”. At this time, one notch appears shown in Fig. 1.5 (b) which equal to 2.5kHz. Then using a lot of simulations examined to find the notch frequency equation. The position of notch changes depending on the modulated value. When frequency f=1kHz situation, set one square equal to 200𝜇𝑠, the width before modulation is W, and after modulation is 𝑊_𝑀. Notch can be created as following [21]:

(5 200 )

( ) 400

notch

M

kHz s k

f k

W W s

  





 ^(1.1)

where the notation 𝑘 denotes a positive integer. When 𝑘 = 1, a notch is created at 2.5kHz which is the same as Fig. 1.5 (b). According to Eq. 1.1, the notch frequency is decided by only the difference of the pulse width. At here, predecessors developed an algorithm that uses ∆Σ modulation to spread the clock spectrum while allowing us to select the bands that we do not want to spread. We find that the notch characteristics can be applied in DC-DC switching converter to reduce EMI. Furthermore, the noise component of a specific frequency could be suppressed.

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Figure 1.5 Spectrum of PWM using PWM ∆Σ DTC.

1.3 Organization of Dissertation

In this dissertation, we try to consider about some spread spectrum techniques for EMI reduction with suppressing diffusion of power supply noise and output ripple decrease.

We discuss various kinds of DC-DC converter, and create methods in order to reduce EMI noise. Moreover, we propose a spread spectrum technique for clock pulse with suppressing diffusion of power supply noise using pulse width coding methods, based on the notch characteristics design. We expect that if notch frequency is set to the frequency of the received signal by adjusting the clock frequency. Therefore, just let the notch frequency be equal to the received signal frequency, and it will suppress noise in the received signal frequency and be not affected by other spread spectrum as we mentioned in section 1.2.

Chapter 1 introduces the background, the motivation and the objectives of this research. Chapter 2 discusses the basic topology and basic operation of DC-DC switching converter, and also discusses other types of switching power supply such as hysteretic control converter and soft switching converter and illustrates their merits and demerits. Chapter 3 presents proposes EMI reduction and creates output ripple decease method. Chapter 4 discusses notch frequency method with pulse coding control in DC-DC buck converter. Chapter 5 creates a full-automatic notch generation of pulse width coding switching converter. Chapter 6 confirms the notch frequency experimentally with the prototype circuit. Chapter 7 summarizes conclusions obtained through this research.

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2. Conventional DC-DC Switching Converter

The DC-DC converter is the power converter of the switching power supply. Normally, a DC-DC converter is constituted by switching element (such as transistor and diode), inductor and capacitor. There are three available basic topologies according to the way of the inductor connection: buck converter (step-down type), boost converter (step-up type) and buck-boost converter (invert type). This chapter reviews their fundamental and also discusses other type of switching power supply such as hysteretic control converter and soft switching converter and illustrates their merits and demerits.

2.1 Basic Topology

DC-DC switching converter can be classified in terms of functions and operating methods, as shown in Fig. 2.1. A DC/DC switching converter can step down or step up the input voltage. As an extension of this capability, buck/boost conversion is also possible.

Pulse Width Modulation (PWM) and Pulse Frequency Modulation (PFM) are among the operation modes to control the output voltage. PWM provides regulation by adjusting the on/off time ratio at a constant switching cycle (frequency), whereas PFM uses a fixed on/off time ratio and a variable frequency. Also, a current mode, a voltage mode, and a hysteretic (or ripple, or comparator) control mode are among the available feedback control methods designed to regulate the output.

Switching converter is configured by a combination of these elements. The optimal combination must be selected based on the intended application, input/output conditions, design specifications and performance goals, cost, size and other restrictions to be met.

The designer needs to know the characteristics as well as pros and cons of each element.

We hope to design the low noise, high efficiency, low cost, compact, small ripple, low power consumption and fast response switching converter by combining various factors.

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Figure 2.1 Performance of DC-DC switching converter.

Fig. 2.2 shows the basic configuration of a DC-DC converter. A typical DC-DC switching converter includes a detection circuit, a reference voltage, an error amplification circuit, a PWM modulation circuit, a drive circuit, and a power stage. First, the DC input voltage is controlled by the power stage of the DC-DC converter. By this, it is converted into a high-frequency square wave. DC voltage output is obtained by smoothing this square wave. The output voltage is detected by the feedback circuit and compared with the reference voltage to amplify the error voltage. Then, according to the magnitude of the amplified error voltage, the PWM modulation circuit controls the on / off ratio of the switch through the drive circuit, thereby adjusting the output voltage so as to suppress the error voltage. This is the basic configuration of a DC-DC converter in a typical switching system.

There are three distinct rails possible for an inductor to be connected: the output, the input and the ground in DC-DC converter part. These three connecting ways realize three basic topologies of DC-DC switching converter. They are buck converter, boost converter and buck-boost converter respectively, as shown in Fig. 2.3.

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Figure 2.2 Basic configuration of DC-DC switching converter.

Figure 2.3 Basic constitution of buck, boost, and buck-boost converters.

In the case of a PWM converter, the voltage applied to the switch and the waveform of the current flowing through the switch are approximately square waves, and Fig. 2.4 shows the operation of the switch SW, the current flowing through the switch 𝑖_𝑠𝑤, and the waveform of the voltage applied to the switch 𝑉_𝑠𝑤. Define the on-duty ratio 𝐷 and off-duty ratio 𝐷^′ as Eq. 2.1 and 2.2. Here, 𝑇_𝑠 is a switching cycle, 𝑇_𝑜𝑛 is a switch-on period and 𝑇_𝑜𝑓𝑓 is a switch-off period.

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Figure 2.4 Switch state and switching waveform.

on on

s on off

T T

D T T T

 (2.1)

' 1

D  D

' off off

s on off

T T

D  T T T

 (2.2)

2.2 Basic Operation of DC-DC Switching Converter

2.2.1 Basic Operation of Buck Converter

Next, the operation of the most basic buck converter among DC-DC converters is explained. Figs. 2.5, 2.6, 2.7 show the basic circuit of a buck converter, and Fig. 2.8 shows its timing chart. This circuit contains a main power switch SW, a freewheeling diode D, an inductor L, an output capacitor C and a load resistor 𝑅_𝐿. When the switch SW is on, the current is supplied from the input voltage 𝑉_𝑖 to the output through the inductor L. At this time, the increase in the current ∆𝐼_𝐿 flowing through the inductor is given by the following:

i o

L on

V V

I T

L

   

(2.3) On the other hand, when SW is off, the current flowing in inductor 𝐼_𝐿 is supplied to the load via D. At this time, the increase in the current ∆𝐼_𝐿 flowing through the inductor is given by the following:

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o

L off

I V T

   L 

(2.4) In the steady-state, the amount of change in the inductor current during the on-period and the off-period is equal, so the following equation holds from (2.3) and (2.4).

i o o 0

on off

V V V

T T

L L

    

(2.5) Rearranging Eq. 2.5, the following can be given:

o i

V D

V  (2.6)

The above equation shows the relationship between the input/output voltage ratio and the duty ratio in the buck converter. From these relationships, it can be seen that the buck converter can control the output voltage by controlling the duty ratio.

Figure 2.5 Basic circuit of buck converter.

Figure 2.6 Buck converter when switch (SW) turns on.

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Figure 2.7 Buck converter when switch (SW) turns off.

The inductor current, the capacitor current and the output voltage is showing in Fig.

2.6. When the switch is on, the inductor current increases with the slope (𝑉_𝑖 − 𝑉_𝑜)/𝐿.

When the switch is off, the inductor current decreases with the slope 𝑉_𝑜/𝐿. Since the voltage on the filter capacitor is equal to the output voltage, the voltage change across the capacitor is actually the ripple voltage of the output voltage.

Figure 2.8 Timing chart of buck converter (continuous current mode (CCM)).

Fig. 2.8 shows a basic block diagram of the buck type DC-DC converter [23]-[24]

with the Pulse Width Modulation (PWM) signal control and Fig. 2.9 shows its main signals. This converter consists of the power stage and the control stage. The power stage contains a main power switch SW, a freewheeling diode D, an inductor L, an output capacitor C and a load resistor R. The main switch is controlled by the PWM

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signal from the control stage, which consists of an operational amplifier AMP, a comparator Comp and a reference voltage source 𝑉_𝑟. First, when the PWM signal is high, the switch signal SW is turned on and the output voltage rises. Therefore, the error voltage ∆𝑉 is reduced and the duration of the PWM signal in high is shortened. To make the off-time of switch SW longer, the output voltage 𝑉_𝑜 is going to decrease. As 𝑉_𝑜 decreases, the error voltage ∆𝑉 increases. Therefore, the duration of the PWM signal at the low state is shortened. To make the on-time of the PWM signal SW longer, 𝑉_𝑜 increases. By repeating this operation, 𝑉_𝑜 is kept to be constant. The comparator Comp generates the PWM signal by comparing a saw-tooth signal SAW and the amplified error voltage ∆𝑉 as shown in Fig. 2.10. The saw-tooth generator resets and starts when the clock pulse rises.

Figure 2.9 Voltage-mode negative feedback control circuit.

Figure 2.10 Waveforms in switching converter.

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2.2.2 Power Stage Transfer Function of Buck Converter

Since the DC-DC converter is a power circuit using negative feedback control, its stability is determined by the loop gain. However, it is not easy to derive the loop gain of DC-DC converter. Because the power stage of the DC-DC converter has two different operating states when the switch is on and off, the transfer function cannot be derived simply. Generally, the state-space averaging method [22] is used to derive the transfer function of the power stage in a DC-DC converter. So in the following, we will derive the transfer function of the power stage in the buck converter.

Fig. 2.11 shows the basic circuit of the power stage with equivalent resistance in the buck converter. This buck converter can be represented by the equivalent circuit by dividing it into an on-period and an off-period. Fig. 2.12 shows the equivalent circuit during the on-period, and Fig. 2.13 shows the equivalent circuit during the off-period.

At here, 𝑟_𝑠 is the equivalent resistance of switch SW1, 𝑟_𝑑 is the equivalent series resistance of diode D, and 𝑟_𝐿 is the equivalent series resistance of inductor 𝐿. Here, the state equation is established on the assumption that the buck converter shown in Fig.

2.11 operates in the continuous current mode (CCM). Then we define state variables of inductor current 𝑖_𝐿 and capacitor voltage 𝑉_𝑐. Then, apply Kirchhoff's voltage law to the equivalent circuit of the on-period and the off-period, and derive the state equation in each period. In the following sections, we derive the state equation, the static and dynamic characteristics, and finally the transfer function of the converter.

Figure 2.11 Basic circuit of power stage.

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Figure 2.12 On-period equivalent circuit.

Figure 2.13 Off-period equivalent circuit.

First, let us derive the state equation. Deriving on-state equation according to Fig. 2.12 and applying Kirchhoff's voltage law and current measurement to the inductor current 𝑖_𝐿 and capacitor voltage 𝑉_𝑐 gives the following equation:

1 1

s L

L

L c i

r r

di i V V

dt L L L

     

(2.7)

1 1

c

L c

dV i V

dt  C CR

(2.8) Here, Eq. 2.7 and 2.8 using the state vector 𝑿 = [𝑖_𝐿

𝑉_𝑐] can be expressed as the following:

1 1 i

dX A X B V dt  

(2.9)

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1 1

0

L L s

L

i c

c

di r r

dt L L i

L V V

dV

C RC

dt

       

       

       

       

   

 

(2.10)

Eq. 2.10 is the on-state equation in buck converter. Then using the same method can derive the off-state equation according Fig. 2.13.

2 2 i

dX A X B V dt  

(2.11)

d L 1

L

L c

r r

di i V

dt L L

    

(2.12)

1 1

c

L c

dV i V

dt  C CR

(2.13) So the off-state equation in the buck converter is like in the following Eq. 2.14.

1

0

1 1 0

L L d

L

i c

c

di r r

dt L L i

V V dV

C RC

dt

     

       

 

       

 

     

   

 

(2.14)

The weighted average of the state equation for the on-period and off-period at the duty ratio D becomes the following equation:

' '

1 2 1 2

( ) ( ) _i _i

dX DA D A X DB D B V AX BV

dt      

(2.15) Here, each coefficient matrix of Eq. 2.15 is:

'

1

1 1

1 1 1 1

L s L d

r r r r r

L L

L L L L

A D D V

C RC

C RC C RC

 

        

     

      

        

     

   

(2.16)

(

'

1 0

0 0 0

D

B D L D L

     

   

         (2.17)

Here, 𝑟 = 𝑟_𝐿+ 𝐷 ∙ 𝑟_𝑠+ 𝐷^′∙ 𝑟_𝑑.

Then, let us show the static characteristics equation in the buck converter. In the static state, state variables and parameters do not change, as shown in the following equation:

i 0 dX AX BV

dt   

(2.18)

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According to Eq. 2.18, we can get 𝑿 = −𝑨⁻¹∙ 𝑩 ∙ 𝑉_𝑖. So X can be expressed as follows:

' '

/ 1

1 /

1

i o

X D DV D R Z R

 

 

   

  (2.19)

Here 𝑍_𝑜 is the internal resistance of the buck converter and is given by the following equation:

'

o s D L

Z Dr D r r

(2.20) Next, small signal dynamic characteristics is shown when the input voltage, duty ratio and load resistance are subjected to small deviations [22]-[25].

1 1

0 1 1

1 0 0 0

d s

i

r r

X s CR L

X L V r L

D s

C L

         

 

         

         

(2.21)

1 1

1 /

1

1 0

d s

i

r r r R

s CR L

LR LD V s r

C L

        

    

        

(2.22)

1 / (1 )

1 ( ) /

1 ( ) (1 / )

o L d s

o

R CR

V r r R

P s D Z R

   

 

   

(2.23) Here, 𝑃(𝑠) = 1 + 2𝛿(𝑠/𝜛_𝑛) + (𝑠/𝜛_𝑛)². In the buck converter, 𝛿 = (1/𝐶𝑅+𝑍_𝑜/𝐿)/

𝜛_𝑛, 𝜛_𝑛 = √(1 + 𝑍𝑜/𝑅)/𝐶𝑅 [26]. Eq. 2.24 is a transfer function that indicates the change in output voltage 𝑉_𝑜 with respect to the change in duty ratio D.

1 ( ) /

( ) (1 / ) ( )

o o L d vdo

o

V V r r R G

D P s D Z R P s

    

  (2.24)

Using the same method, Eq. 2.25 is a transfer function that indicates the change in output voltage 𝑉_𝑜 with respect to the change in input voltage 𝑉_𝑖.

( ) (1 / ) ( )

o o vvo

o

V V D G

D P s Z R P s

  

  (2.25)

Eq. 2.26 is a transfer function that indicates the change in output voltage 𝑉_𝑜 with

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respect to the change in resistance R.

/ 2

(1 / ) (1 / )

( ) (1 / ) ( )

o o o vro

o vr

o

V V Z R G

s L Z s

R P s Z R P s

      

   (2.26)

In the case of a switching power supply, the duty ratio D, the load resistance R, and the input voltage 𝑉_𝑖 are considered as external parameters, and Fig. 2.14 shows a block diagram of the buck converter. The error voltage amplifier and PWM converter in the control circuit are linear conversions and can be replaced by a constant K. Here, the transfer function of the phase compensation circuit performed by the error amplifier is not described. At this time, the loop transfer function 𝐺_𝑜(𝑠) is basically a quadratic equation, in an actual circuit, a phase delay occurs due to a delay caused by discrete control of an amplifier and a PWM signal, and the power supply system tends to be unstable. In Fig. 2.14, the load current fluctuation is equivalently indicated by load resistance change Δ𝑅 and input voltage change is indicated by Δ𝑉_𝑖. The block after the power supply 𝑃(𝑠) represents the effect of the output impedance 𝑍_𝑜 on the actual power supply.

Figure 2.14 CCM block diagram of buck converter.

At last, the characteristics of the buck converter is analyzed with the simulation software SIMPLIS. The parameters used there are shown in Table 2.1 and the loop transfer function is shown in Fig. 2.15 using a Bode diagram. Here, the internal resistance of the switch and inductor are 50mΩ and 10mΩ, the ESR of the capacitor is 220mΩ, and the GB product of the operational amplifier is 100 MHz. From Fig. 2.15 we can found that the phase margin is about 50 degrees. The gain changes at the frequency where the phase becomes 90 degrees, and we can find that the resonance phenomenon occurs at 1.50kHz. According to the transfer function, the resonance

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frequency𝑓 = ¹

2𝜋√𝐿𝐶 = ¹

2𝜋√50×10⁻⁶×220×10⁻⁶ = 1.52𝑘𝐻𝑧 is obtained, which roughly equal to the value on the Fig 2.15.

Table 2.1 Parameters of the buck converter.

𝑉_𝑖 𝑉_𝑜 𝐼_𝑜

10V 5V 0.5A

𝐿 𝐶 𝐹_𝑐𝑘 50μH 220μF 500kHz

Figure 2.15 Bode diagram of the buck converter.

2.2.3 Boost Converter

In the following, the operation of the boost converter is explained. Figs. 2.16, 2.17, 2.18 shows the basic circuit of the boost converter, and Fig. 2.19 shows the timing chart of the boost converter under steady state. Similar to the buck converter in previous section, the switch can be set at two positions alternately, and the circuit operates at on-state and off-state accordingly, as shown in Fig. 2.17 and Fig. 2.18.

When the switch SW is on, the energy storage in coil and the inductor current increases by the slop 𝑉_𝑖/𝐿. When switch SW is off, the inductor current decreases by the slope (𝑉_𝑜− 𝑉_𝑖) /𝐿.

When the switch SW is on, the increase in the current ∆𝐼_𝐿 flowing through the inductor is given by following:

i

L on

I V T

  L 

(2.27) On the other hand, when SW is off, supply energy to the load via D from power supply

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E and coil L. At this time, the increase in the current ∆𝐼_𝐿 flowing through the inductor is given by following:

o i

L off

V V

I T

L

    

(2.28) According to the steady-state principle of the inductor volt-second balance, the relation between the input voltage and the output voltage is obtained

( )

o i off 0

i on V V T

V T

L L

 

   _(2.29)

Rearranging Eq. 2.29, the following can be given:

'

o s 1

i off

V T

V T  D (2.30)

The above equation shows the relationship between the input/output voltage ratio and the duty ratio in the boost converter. From these relationships, it can be seen that the output voltage 𝑉_𝑜 of the boost converter must be larger than the input voltage 𝑉_𝑖.

Figure 2.16 Basic circuit of the boost converter.

Figure 2.17 Boost converter when switch (SW) turns on.

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Figure 2.18 Boost converter when switch (SW) turns off.

Figure 2.19 Timing chart of the boost converter (CCM).

2.2.4 Buck-boost converter

The converters in Figs. 2.20, 2.21 and 2.22 are boost converter. When the switch SW is on, the inductor current increases by the slope 𝑉_𝑖/𝐿. When the switch SW is off, the inductor current decreases by the slope 𝑉_𝑜/𝐿. The timing chart of the buck-boost converter under steady state is as shown in Fig. 2.23.

When the switch SW is on, the increase in the current ∆𝐼_𝐿 flowing through the

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inductor is given by the following:

i

L on

I V T

  L 

(2.31) On the other hand, when SW is off, the increase in the current ∆𝐼_𝐿 flowing through the inductor is given by the following:

o

L off

I V T

   L 

(2.32) In the steady-state, the amount of change in the inductor current during the on-period and the off-period is equal, so the following equation holds:

i o 0

on off

V V

T T

L  L  

(2.33) Rearranging Eq. 2.33, the following can be given:

'

o on

i off

V T D

V T  D (2.34)

From Eq. 2.34, we can know that the output of buck-boost converter is an inverting voltage. When 0 ≤ D < 0.5, the output voltage is reduced. When 0.5 < D ≤ 1, the output voltage is amplified. Also when D = 0.5, we can get 𝑉_𝑜 = −𝑉_𝑖.

Figure 2.20 Basic circuit of the buck-boost converter.

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Figure 2.21 Buck-boost converter when switch (S) turns on.

Figure 2.22 Buck-boost converter when switch (S) turns off.

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Figure 2.23 Timing chart of the buck-boost converter.

2.3 Hysteretic Control Switching Converter

Roughly, there are two control methods for stabilizing the operation of the DC-DC converter; linear control and nonlinear control. Linear control is such as voltage mode control and current mode control. The output voltage is stabilized by adjusting the timing at which the switching element is turned on and off using a fixed-frequency PWM (pulse width modulation) signal, which is used in a very wide range of fields from portable electronic devices to industrial electronic devices. That is, it can be applied to both low power output and high power output. However, it has the disadvantage that the response speed to sudden changes in load is relatively slow. Its reasons are delay due to the frequency characteristics of the error amplifier in the feedback loop, dead time delay equivalent to one cycle of the switching operation, and delay due to the frequency characteristic of the phase compensation circuit including the LC filter. Nonlinear control such as hysteretic controlled has the advantage of high response speed to sudden load changes and it can be realized with a simple circuit configuration.